A geometric progression series has first term 2 with common ratio as -1/2(x + 1). When x becomes 1/3, find the sum of all odd-numbered terms of the series. Answer given as 18/5 - not sure that it is correct! Thanks
So the odd numbered terms are which are the first, third, and 5th terms and so on
So this is just a geometric series with the ratio = so when
The ratio is
So the sum of a geometric series with ratio = is
Sorry I didn't see that the first term was 2, being as this is the case the answer must be doubled and we get the correct answer
plug in x = 1/3, you find that r = -2/3
now, we want all odd terms, first note that these are the positive terms, secondly, note that the common ratio between consecutive odd terms is r^2. i hope you can see why. hence, the odd terms form a geometric series with first term a = 2 and common ratio r = 4/9. you should be able to do the rest. we get 18/5 as desired